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Directions: When attempting to prove triangles congruent,
it is important to satisfy all of the conditions of the congruent triangle method
you are using. This activity is designed to help
you organize your thinking about how the parts of a congruent triangle
proof will come together. In each problem below, examine
the diagram and the GIVEN information. You may wish to draw the
diagrams on paper so that you can mark off the information.
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Determine the method needed to prove the triangles
congruent.
(ASA, SAS, AAS, SSS, or HL for right triangles only)
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Check to see if you have the correct method by looking at
the Method for Congruent Triangles box at the bottom of the chart.
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Each of the three components needed to support the chosen
method appear to the left of their corresponding
Statement.
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Decide what Reasons can be used to support your
decisions.
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This first problem is an
easy problem designed to let you see how this activity is going to
work. Look carefully at the problem before continuing.
If you click on the answer in the drop down box, it will remain
visible. |
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Method |
Statements |
Reasons |
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Method |
Statements |
Reasons |
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4.  |
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Method |
Statements |
Reasons |
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Method |
Statements |
Reasons |
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(Problem #5 could also have been solved using SAS and the vertical angles.)
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Method |
Organized Thinking |
Supporting Reason |
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(Be careful with problem #6.
Remember that ASS (the Donkey Theorem) does not work to prove
triangles congruent.)
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In each of these problems,
the 3 components of each congruent triangle method actually APPEARED in
the proof. For example, if SAS was used, the proof
contained two sets of congruent sides (S, S) and one set of
congruent angles (A).
Be sure you satisfy all 3 parts of the
method you are using, BEFORE you state that your triangles are
congruent. |
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